An Introduction to the Mathematics of Biology: With Computer Algebra Models

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Springer, 1996 - Mathematics - 417 pages
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This text has been adopted at: Georgia Institute of Technology, Carnegie Mellon University, University of California at Los Angeles, California State University, Northeastern Illinois University, and University of Colorado. The authors of this new textbook have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another but has a unity of its own. The biology and mathematics are equal; they are complete and flow smoothly into and out of one another. Student response to this approach has been exhilarating to watch as standard, unexciting applications give way to problems of contemporary interest- HIV, genetics and aging, for example. The book has several important features that the authors have developed from their classroom experience. First and foremost, it is designed to be comprehensible to students of biology as well as to students of mathematics and related physical sciences. No prior study of biology is necessary and only a year of calculus is required. The mathematics proceeds from simple to more complex concepts, and the biology proceeds from the population level down to the molecular level. This arrangement makes the material accessible to most biology majors and to most mathematics students near the beginning of their mathematical studies. A unique feature of the book is the use of a computer algebra system, Maple, in parts of every chapter. This hands-on approach to computation provides a rich source of information through the use of 'what-if' scenarios and thus allows students to grasp important biological and mathematical concepts in a way that is not possible without such technology. For students who do not have access to a computer algebra system, each topic is complete without the use of either numerical or symbolic equations. Graphic visualizations are provided for all the mathematical results. The text has extensive exercises, problems and examples, along with references for further study. It will be of interest to any mathematics department that teaches mathematical biology. It also lends itself to self-study for more advanced mathematicians and scientists who wish to explore further this most exciting frontier in the applications of mathematics and computers to the natural sciences. CONTENTS: Preface Acknowledgements Biology, Mathematics and a Mathematical Biology Laboratory Some Mathematical Tools Reproduction and the Drive for Survival Interactions Between Organisms and Their Environment Age-Dependent Population Structures Random Movements in Space and Time The Biological Disposition of Drugs and Inorganic Toxins Neurophysiology The Biochemistry of Cells A Biomathematical Approach to HIV and AIDS Genetics Index

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About the author (1996)

Ronald W. Shonkwiler is a Professor in the School of Mathematics at the Georgia Institute of Technology. He has authored or co-authored over 50 research papers in areas of functional analysis, mathematical biology, image processing algorithms, fractal geometry, neural networks and Monte Carlo optimization methods. His algorithm for monochrome image comparison is part of a US patent for fractal image compression. He has co-authored two other books, An Introduction to the Mathematics of Biology and The Handbook of Stochastic Analysis and Applications.

James Herod joined the struggle against capitalists, politicians,
and priests (or, to use the abstractions, capital, state, and god)
during the social upheavals of 1968 and has remained in it ever since.

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